I'd caution against the urge to buy really big colonies to start off with. Yes, it can work, but there are a couple of big problems.
The first that you'll notice is cost. Getting a full colony is far more expensive than buying a frag and growing it out yourself. A frag of a basic acropora coral might cost $50; a mother colony of the same coral could easily go for $300-$500.
But that's not really the biggest problem. The real problem is that corals are sessile animals. Where most animals adapt to their environment by changing where they are, corals can't do that. They adapt to their environment by changing how they grow. And a big coral colony that you bring in isn't adapted to your conditions; its adapted to wherever it grew. You are likely to have quite a bit of die-off when transplanting a big colony, especially if it's something like an acropora.
But if you don't want to go the SPS route, there are plenty of LPS/Softies that have that full look to them, you just have to know what to look for.
First, leather corals will give you a lot of that. Toadstool corals are virtually indestructible and can grow to an absolutely massive size. In my tank, I have a toadstool that's about 8" across, and it itself is a self-frag from a colony that was about 14" across. In my other tank, I have a different color morph of toadstool that's about 12" across. Put a few of those in your tank and you'll have a lot of lush coral growth. Or you could just put in one and give it time, and it'll spread throughout your tank.
Spaghetti/Devil's Hand leathers give an acropora-esque look while having the resiliency and growth of a softie. The colors are more pastel and less diverse than a proper acro, but they get bigger faster and have the same tree-like growth form as acros.
Zoas will form dense mats in good conditions, giving an appearance similar to an encrusting monti but with much more vibrant and varied color patterns. And mushroom corals will spread and obscure bare rock, again contributing to that lush look.
And if you really want to go nuclear, add in some GSP or Xenia family corals. They'll grow really fast, give you a lush, lived-in look, and honestly a colony of pulsing xenia is absolutely mesmerizing to watch. I personally prefer the subtler look of SPS corals, but if you want a faster "full tank" look, you can get quite a bit of mileage out of softies. Toss in a few impact LPS - like some lobos, torches, hammers or goniopora - and you can have a really nice looking tank without having to plan around SPS corals.